2 Answers
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Funny thing is, both of those have the exact same quantum numbers - parity, spin, baryon number and the rest. So a neutral pion can be a mixture of (u + anti-u) and (d + anti-d). There actually result two types of neutral "pion" that decay differently. One is actually heavier, and we call it the eta meson.

Oops I didn't mention yet the strange and anti-strange quark combination, which also gets tangled into the mixes... but it's not important to the neutral pion.

The Particle Data Group represents the valence content of the neutral pion as $(u\bar{u} - d\bar{d})/\sqrt{2}$. This is, as Daren says, a somewhat arbitrary choice.
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dmckee♦Mar 13 '11 at 3:40

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Dear @DarenW, I gave you +1 but your formula for the eta mesons is wrong. The right one includes at least an equal mixture of the strange-antistrange quark pair, see the upper right corner of en.wikipedia.org/wiki/Eta_meson - At this mass level, one has to think about the whole SU(3) symmetry mixing the three light quark flavors u,d,s, so there are more basis vectors for the mesons. ... Oh, I just noticed you have corrected yourself, too, so I do it in the same way haha.
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Luboš MotlMar 13 '11 at 6:50

Eh, so I'm a little out of practice. As long as the eta mesons know how to be eta mesons...
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DarenWMar 22 '11 at 6:29

They're made of a combination of up and anti-up, down and anti-down, and strange and anti-strange. And that's just to begin with. To be perfectly accurate you'd have to add all six quarks (okay, maybe not the top).

The short reason is that all these quark combinations have the right quantum numbers and so are included. Feynman diagrams of all sorts contribute, for example:

In the above, the wavy lines are virtual vector bosons. I've put two in because, as Anna V notes, the pion is a psuedoscalar and so has zero spin. Of course the heavy quarks don't appear very much in a light meson since they have to be made from borrowed energy.

People aren't much interested in the heavy quark contribution to the pion. An analogous subject is the heavy quark content of the proton and a reference which will illustrate how this comes about is:
10.1103/PhysRevD.70.094028, Andrei Kryjevski, Heavy Quark $\bar{q}q$ Matrix Elements in the Nucleon from Perturbative QCDhttp://arxiv.org/abs/hep-ph/0312196

Note that the masses of the nucleons are about 1 GeV while the mass of the t-quark is around 171 GeV.

Hmm. A pi0 is a pseudoscalar, so the diagram you show is a bit misleading, since we are discussing the pi0. Come to think of it may be that is why the -sign in the linear combination was chosen, for first order diagrams.
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anna vMar 13 '11 at 8:09